A069148 Numbers k such that k*k!/A062758(k) is not an integer where A062758(k) is the product of squares of divisors of k.

4, 6, 8, 10, 14, 16, 18, 20, 22, 26, 28, 34, 38, 42, 44, 46, 52, 58, 62, 66, 68, 74, 76, 78, 82, 86, 92, 94, 102, 106, 114, 116, 118, 122, 124, 134, 138, 142, 146, 148, 158, 164, 166, 172, 174, 178, 186, 188, 194, 202, 206, 212, 214, 218, 222, 226, 236, 244, 246

Offset: 1

Author

Benoit Cloitre, Apr 08 2002

Keywords

• easy
• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Complement of A069149.

Cf. A001563 (n*n!), A062758.

Programs

Mathematica

Rest[Position[Table[(n*n!)/(Times@@Divisors[n])^2,{n,250}],?(!IntegerQ[ #]&)]//Flatten] (* _Harvey P. Dale, Apr 24 2019 *)
Select[Range[250], !Divisible[#!, #^(DivisorSigma[0, #] - 1)] &] (* Amiram Eldar, Jul 07 2022 *)

PARI

for(n=1,320,if((n*(n!))%(n^numdiv(n))>0,print1(n,",")))